We investigated, using meta-analysis of empirical data and population modelling, plausible scenarios for the cause of late Pleistocene global mammal extinctions. We also considered the rate at which these extinctions may have occurred, providing a test of the so-called 'blitzkrieg' hypothesis, which postulates a rapid, anthropogenically driven, extinction event. The empirical foundation for this work was a comprehensive data base of estimated body masses of mammals, comprising 198 extinct and 433 surviving species > 5 kg, which we compiled through an extensive literature search. We used mechanistic population modelling to simulate the role of human hunting efficiency, meat off-take, relative naivety of prey to invading humans, variation in reproductive fitness of prey and deterioration of habitat quality (due to either anthropogenic landscape burning or climate change), and explored the capacity of different modelling scenarios to recover the observed empirical relationship between body mass and extinction proneness. For the best-fitting scenarios, we calculated the rate at which the extinction event would have occurred. All of the modelling was based on sampling randomly from a plausible range of parameters (and their interactions), which affect human and animal population demographics. Our analyses of the empirical data base revealed that the relationship between body mass and extinction risk relationship increases continuously from small- to large-sized animals, with no clear 'megafaunal' threshold. A logistic ANCOVA model incorporating body mass and geography (continent) explains 92% of the variation in the observed extinctions. Population modelling demonstrates that there were many plausible mechanistic scenarios capable of reproducing the empirical body mass-extinction risk relationship, such as specific targeting of large animals by humans, or various combinations of habitat change and opportunistic hunting. Yet, given the current imperfect knowledge base, it is equally impossible to use modelling to isolate definitively any single scenario to explain the observed extinctions. However, one universal prediction, which applied in all scenarios in which the empirical distribution was correctly predicted, was for the extinctions to be rapid following human arrival and for surviving fauna to be suppressed below their pre-'blitzkrieg' densities. In sum, human colonization in the late Pleistocene almost certainly triggered a 'blitzkrieg' of the 'megafauna', but the operational details remain elusive.